Offset simply refers to how far the mounting surface of the rim is from the true centerline of the wheel. If you took a look at a wheel with a 0 offset, it would mount dead-center from the centerline. A 7" wide wheel running a +45 offset, as per Rishie's fitments, means that the rim is 7" wide, and the center of the wheel is 45mm closer to the outboard (away from the center) of the car.
The key with offset is to get the wheels out on the corners as far as you can without rubbing. This allows you to have a nice stance, which affects how fast the car responds to turn-in, and how much it can balance on the outer tire. Loading up a tire that is more inboard (toward the center of the car) means that you have weight tipping over the center of the tire, which means it may be more likely to roll. Outboard more, the tire won't try and tuck as much.
Camber also comes into play here. Negative camber is very useful under hard cornering, as under neutral camber, when you're turning, your wheel and tire will tend to droop like this, where the /'s are the tires:
/-----/
That's if you had neutral camber, like this:
|-----|
Now, if you apply some negative camber, your wheels are facing like this (Though don't do this; This range would be what it looked like if you had over 3 degrees of camber or so.
This is just an example of the directions):
/-----\
So, when you cornered, this would happen instead:
/-----|
If you'll notice, your weight is now shifted toward the center of the contact patch more. Something to keep in mind with wheels and tires as well.
Typically, lighter weight wheels will afford you faster acceleration and better handling. However, tires are your actual INTERFACE between the car itself and the road, so that, too, is VERY important. Get good tires, in other words.
As for the size of the tires, it can be read this way:
195/50 R 16
The first number is the width of the tire in millimeters. This tire would be 195 millimeters wide.
The second number is the percentage of the width that dictates how large the sidewall is. This would be 50 percent. What this means is you take 50 percent, or half, of 195, and that leaves you with 97.5mm of sidewall. This is not the total height of your wheel and tire, but rather JUST one portion of the sidewall.
The last number is the diameter in inches of the wheel that you'll be mounting to. In this case, 16 inches.
Now, the larger sidewall you go with, the more sidewall flex you'll get, as was mentioned. More roll, and so-on. If you went with a 205/50R16 tire on the previous example, you would have 5mm more sidewall height, as it would be 10mm wider. That's 5 more millimeters that it has to flex.
ALSO, by doing this, you're increasing the diameter that the wheel has to travel to make one complete rotation, so the car will rev slower while going faster, which in turn also throws off the speedometer. Though a subtle change like that won't make much more of a difference, I generally try to go with an overall smaller diameter tire to try and shorten the gears, to increase acceleration further.
Whew... If you have any more questions, or you want links to sites where you can either read more of this stuff, or calculators to determine variances in tire size, and the effect on speedometer readings and so on, just ask. I'll post them here, if you want. =)